Tree amalgamations and quasi-isometries

2018/12/12 by Matthias Hamann, Hamann, Matthias · 1 citation
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1812.04987

openalex publication_date 2018/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the connections between tree amalgamations and quasi-isometries. In particular, we prove that the quasi-isometry type of multi-ended accessible quasi-transitive connected locally finite graphs is determined by the quasi-isometry type of their one-ended factors in any of their terminal factorisations. Our results carry over theorems of Papsoglu and Whyte on quasi-isometries between multi-ended groups to those between multi-ended graphs. In the end, we discuss the impact of our results to a question of Woess.

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• Tree amalgamations and hyperbolic boundaries

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